Hi Dave!
On 3 Jul., 15:57, daveloeffler <dave.loeff...@gmail.com> wrote:
> I'd advocate (2), with all cyclotomic fields (of given order) in Sage
> corresponding to the same one in Gap. I doubt this would be much of a
> problem with breaking existing code given the coercion thing I
> mentioned above.
Well, it could be a problem if some code expects that the generator of
gap(K) has the same name as the generator of K, which is currently the
case, but which would be impossible (or not?) if gap(K) was
gap('CyclotomicField(...)').
It seems to me that the element constructor of K bevaves well (at
least with the patch from #8909): K(gap(x))==x for any element of K,
regardless whether the generator of gap(K) is called zeta3 or E(3).
So, one could simply try to implement a genuine _gap_init_ and see
whether all doctests still pass. Hopefully the doctest coverage is
good enough...
Concerning coercion: Right, having coercion in both directions would
certainly justify to have gap(K)==gap(L).
Cheers,
Simon
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